Magnetic Flux Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The magnetic flux through a surface is calculated with Φ = B × A × cos(θ), where B is the magnetic field, A the surface area, and θ the angle between the field and the surface's normal. For a 0.5 T field perpendicular to a 2 m² surface, the magnetic flux equals 1 weber (Wb).
Explanation
Magnetic flux measures how much magnetic field actually passes through a given surface: it depends not only on the field's strength and the surface's size, but also on their relative orientation. When the magnetic field is perfectly perpendicular to the surface (θ = 0°), the flux is maximal, since all the field lines pass straight through it; as the surface tilts relative to the field, fewer and fewer field lines actually cross it, until at 90° (field parallel to the surface), the flux becomes exactly zero — no field line crosses the surface then, they simply slide along it. This same mathematical structure (a quantity, multiplied by an area or a distance, multiplied by the cosine of an orientation angle) appears in several other physics contexts on this site: our kinetic energy calculator shares the same energy-from-motion logic, and the projection by an angle cosine shows up again in our Coulomb's law calculator whenever force components along a direction matter. Magnetic flux is the central quantity of electromagnetic induction: it's precisely its VARIATION over time that generates an induced electrical voltage in a circuit, the physical principle at work in electric generators, transformers, and induction cooktops.
Example: a 0.5 T field perpendicular to a 2 m² surface
Inputs
Magnetic field: 0.5 T. Area: 2 m². Angle: 0° (perpendicular).
Calculation
Φ = 0.5 × 2 × cos(0°) = 0.5 × 2 × 1 = 1 Wb.
Result
The magnetic flux through this surface is 1 weber.
Frequently asked questions
Why does magnetic flux become zero when the field is parallel to the surface?
Because at that orientation, the magnetic field lines slide along the surface without ever actually crossing it: none of them pass through, exactly like a sheet of paper held parallel to a ray of sunlight casts no shadow on itself. Mathematically, cos(90°) = 0, which directly zeroes out the product regardless of the field's strength or the surface's size.
What is the link between magnetic flux and electromagnetic induction?
Faraday's law, one of the fundamental principles of electromagnetism, establishes that any CHANGE in the magnetic flux through a circuit generates an induced electrical voltage in it — whether that change comes from a magnetic field changing in strength, a surface that moves or rotates, or a change in the angle between the two. It's this principle that lets electric generators convert mechanical motion into electricity, by rotating a coil within a fixed magnetic field.
What unit is magnetic flux measured in?
The unit of magnetic flux in the International System is the weber (Wb), defined as the product of a tesla (the unit of magnetic field) and a square meter (the unit of area) — directly consistent with the formula Φ = B × A × cos(θ), since cos(θ) is a unitless number that doesn't change the result's units.